Sorry to hear you got dumped. It's never a nice experience and you may be feeling that you want to escape, or that no one will ever love you in the way he did.
Truth is, someone will love you for more than he did, because he doesn't see your true potential.
It's his loss, that he lost a beautiful, kind-hearted girl.
To answer your question, I think that inviting someone over to their parents house is wise, especially as 5 months is more than adequate timing.
Were you too pushy? I don't know you or what you're like around people, so I'm not sure.
Sending hugs for you, and I'm here if you ever need a chat.